A simple random sample of size $$ n=50 $$ is obtained from a population whose size is $$ \mathrm{N}=25,000 $$ a (a) Describe the sampling distribution of $$ \hat{p} $$. Choose the phrase that best describes the shape of the sampling distribution. B. Approximately normal because $$ n \leq 0.05 \mathrm{~N} $$ and $$ \mathrm{np}(1-\mathrm{p}) \geq 10 $$ C. Not normal because $$ \mathrm{n} \leq 0.05 \mathrm{~N} $$ and $$ \mathrm{np}(1-\mathrm{p})

Question

A simple random sample of size $$ n=50 $$ is obtained from a population whose size is $$ \mathrm{N}=25,000 $$ a (a) Describe the sampling distribution of $$ \hat{p} $$. Choose the phrase that best describes the shape of the sampling distribution. B. Approximately normal because $$ n \leq 0.05 \mathrm{~N} $$ and $$ \mathrm{np}(1-\mathrm{p}) \geq 10 $$ C. Not normal because $$ \mathrm{n} \leq 0.05 \mathrm{~N} $$ and $$ \mathrm{np}(1-\mathrm{p})<10 $$ D. Not normal because $$ \mathrm{n} \leq 0.05 \mathrm{~N} $$ and $$ \mathrm{np}(1-\mathrm{p}) \geq 10 $$ Determine the mean of the sampling distribution of $$ \hat{p} $$. $$ \mu_{\hat{p}}=\square $$ (Round to one decimal place as needed.)

Franklin Lindsey · Accepted Answer

The sampling distribution of $$ \hat{p} $$ is approximately normal because $$ n \leq 0.05N $$ and $$ np(1-p) \geq 10 $$. The mean of the sampling distribution is $$ p $$.

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